Dynamics of Coupled Oscillator Systems

Abstract

The discussion of dissipative structures appearing in the first five chapters was given in the context of spatio-temporal patterns existing in continuous media. In the present chapter we consider another important class of dissipative systems consisting of a large number of degrees of freedom, those composed of aggregates of isolated elements. A neural network consisting of intricately coupled excitable oscillators (neurons) is one example of such a system. In addition, there are many systems of this type composed of groups of cells exhibiting physiological activity. As the subject of study in nonlinear dynamics has broadened in recent years to include phenomena found in living systems, interest in coupled oscillator systems has grown. In what follows, we consider a relatively simple example forming the subject of a great deal of present study, that of a collection of limit cycles oscillators, and basing our investigation on the method of phase dynamics, we discuss the fundamental points regarding synchronization phenomena.